Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation

Yıl 2019, Cilt: 3 Sayı: 4, 174 - 191, 30.12.2019

Kamel Hamdache Djamila Hamroun

https://doi.org/10.31197/atnaa.512065

Cited By: 1

Öz

The Landau-Lifshitz-Bloch (LLB) equation is an interpolation between Bloch equation  valid for high temperatures and Landau-Lifshitz equation valid for low temperatures. Conversely in this paper, we discuss the behaviours of the solutions of (LLB) equation both as the temperature  goes to infinity or 0.  Surprisingly in the first case,  the
behaviour depends also on  the scaling of the damping parameter $\delta$ and the volume exchange parameter $a$. Three cases are considered and accordingly we get either a linear stationary equation, Bloch equation or Stokes equation.  As for the small temperature behaviour,   $\delta$ and $a$ being independent of the temperature, we show that the limit of (LLB) equation  is  Landau-Lifshitz-Gilbert equation.

Anahtar Kelimeler

Landau-Lifshitz-Bloch equation, Landau-Lifshitz-Gilbert equation, Bloch equation

Kaynakça

• Reference 1: F. Alouges and A. Soyeur, On global weak solutions for Landau-Lifschitz equations : Existence and nonuniqueness, in Nonlinear Analysis, Theory, Methods and Applications, 18 (11) (1992) 1071--1084.
• Reference 2: M. Feischl and T. Tran, Existence of regular solutions of the Landau-Lifshitz-Gilbert equation in 3D with natural boundary conditions, in SIAM J. Math. Anal. 49 (6) (2017) 4470--4490.
• Reference 3: D.A. Garanin, Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets, in Phy. Rev. B 55 (1997) 3050--3057.